dually

Because of this, many theorems about closed sets are dual to theorems about open sets.For example, any union of open sets is open, so dually, any intersection of closed sets is closed.The interior of a set is the largest open set contained in it, and the closure of the set is the smallest closed set that contains it.…

Ellen White's writings are sometimes referred to as the Spirit of Prophecy by Adventists.The term is dually applied to the Holy Spirit which inspired her writings.Early Sabbatarian Adventists, many of whom had come out of the Christian Connexion, were anti-creedal.…

In 1886, she launched Recamier Toilet Preparations, Inc., which she managed and marketed by incorporating her own name on the label and writing strategic, innovative advertising copy.These actions were dually audacious, especially the use of her family name and crest on her products.People of her class were appalled at such indiscretions, but Harriet understood that it actually encouraged women who aspired to a higher social status to purchase her products.…

More generally, given a set S, specifying the set of continuous functions into all topological spaces X defines a topology.Dually, a similar idea can be applied to maps This is an instance of a universal property.Various other mathematical domains use the concept of continuity in different, but related meanings.…

The concert was dually released as a DVD as well as an audio album.The album was released on DVD on the same day as the CD.…

The audition process proved difficult, as some of Akingbola's close friends were also considered for the part.He was dually motivated by the prospect of financial security, and the role itself.Enthused by the character outline, he tailored his performance to the detailed breakdown he was given, and attended his audition dressed in the style he believed Malick would wear.…

However, because the theory argues that people draw on information based on their identities, intersectionality is relevant.For instance, how do people process identities that are dually marginalized (black women)?Are these women (based on cumulative status characteristics) going to be less influential than white women?…

They can also set up a dual verbal-nonverbal memory trace by imaging to concrete words, but this is somewhat less likely than naming pictures, hence the lower memory for concrete words than pictures.Abstract words are difficult to image and hence are least likely to be dually coded.The expected additive memory benefit of dual coding has been confirmed in numerous experiments which also suggested that the nonverbal code is mnemonically stronger (contributes more to the additive effect) than the verbal code.…

Students also have the option of being dually-enrolled, or, remaining students at their home high schools while attending the Academy.However, some private schools will not allow students to remain enrolled while attending the Academy.…

There are several specific causes that are credited to continuing the cycle of the demand for domestic work.One of these causes is that with more women taking up full-time jobs, a dually employed household with children places a heavy burden on parents.It is argued however that this burden wouldn't result in the demand for outside domestic help if men and women were providing equal levels of effort in domestic work and child rearing within their own home.…

The primary source of letters patent in the United States are intellectual property patents and land patents, though letters patent are issued for a variety of purposes.They function dually as public records and personal certificates.In the United States, the forgery of letters patent granted by the President is a crime subject to fine, imprisonment up to ten years or both . Without letters patent, a person is unable to assume an appointed office.…

She was not quite pleased and not altogether offended at his addressing them dually.Cited from The Marquis of Lossie, by George MacDonald

Intuitively, in circumscription a variable is assigned to true only if this is necessary.Dually, if a variable can be false, it must be false.…

Born and raised in Los Angeles, Jonny was dually influenced by music and foreign languages.Coming from a very creative family -- his father, Reuben Klamer, created the classic game The Game of Life and his mother, Shary Klamer (aka, Shary Richards) a former singer/actress/model -- Jonny's musical path was initiated at a very young age.…

It is included on the follow-up release of Raymond v. Raymond, titled Versus.In Japan, the song was released dually with "Never Say Never" as a double A-side single.The song received positive reviews, with critics complimenting the track's dance feel, and the lyrical content.…

A partially ordered set in which all pairs have a join is a join-semilattice.Dually, a partially ordered set in which all pairs have a meet is meet-semilattice.A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice.…

As well, the bullion window, though used lightly, was effective for its limited purpose.These two liquidity measures dually prevented additional failures of major market participants.…

A join-semilattice is bounded if it has a least element, the join of the empty set.Dually, a meet-semilattice is bounded if it has a greatest element, the meet of the empty set.Other properties may be assumed; see the article on completeness in order theory for more discussion on this subject.…

In mathematics, specifically projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting each pair of points.Dually, a complete quadrilateral is a system of four lines, no three of which pass through the same point, and the six points of intersection of these lines.The complete quadrangle was called a tetrastigm by, and the complete quadrilateral was called a tetragram; those terms are occasionally still used.…